A HYBRID ELECTRODYNAMIC VIBRATION HARVESTER
T. Sterken1,2, P. Fiorini1, C. Van Hoof1,2, R. Puers2
1
IMEC vzw, Leuven, Belgium
2
ESAT, Katholieke Universiteit Leuven, Leuven, Belgium
Abstract: A vibration harvester has been designed, combining an electrodynamic transducer with a
micromachined resonator. The transducer consists of 8 off-the-shelf NdFeB magnets floating above a
series of copper coils. The coils are shaped in a meander to optimize the coupling factor of the generator.
The suspension of the magnets is tuned to invoke resonance at the frequency of the targeted vibration,
while the inertia of the magnets is used to improve the energy extraction within a volume of 0.3 cm3.
A prototype has been designed for 1g vibrations at 100 Hz.
Key Words: NdFeB, vibration, harvester
1. INTRODUCTION
Miniature vibration harvesters are being
developed as an alternative to storage based
energy supplies for autonomous electronic
systems, such as wireless sensor nodes or mobile
detectors [1,2]. At present storage based systems,
such as batteries, provide a robust solution, but
their lifetime decreases with their size (and
weight). Miniature systems will thus have a short
lifetime. Furthermore replacing batteries in
autonomous systems is often not economical, and
sometimes even impossible.
The alternatives provided by powerMEMS tackle
this contradiction either by improving the energy
density of the storage medium (e.g. in micro-fuel
cells), either by extracting energy from the
ambient of the autonomous system. The energy
source that is used depends on the application,
ranging from mechanical energy (vibration,
motion) to thermal energy (body heat) or solar
energy. The power necessary for operating
autonomous systems has decreased over time
down to a level of 50 PW.
The harvester proposed in this paper is designed
for vibrations around human activities, by tapping
into a harmonic mode of the electrical grid (e.g.
100 Hz in Europe, 120 Hz in U.S.A.).
Vibration harvesters consist of a transducer that
converts the mechanical power in the motion of
the vibrating object with respect to a nonvibrating reference. It is however not always
feasible to connect a miniature autonomous
system to an external reference. An internal
reference is then created using the inertia of a
seismic mass to transfer the motion of the
vibration towards the energy transducer. A mass
with a higher inertia will provide a better
reference. The following paradox resides in the
use of miniature vibration harvesters: the output
power of the harvester decreases as the
dimensions of the device scale down. As a result
their size is always in the mm range.
Nevertheless miniature harvesters make use of
micromachining and MEMS, because of the
precision, yield and reliability that can be
obtained. A micromachined harvester furthermore
allows a possible integration of the circuitry of the
system into a single system-in-a-package [2]. The
electrodynamic harvester presented in this
contribution combines the advantages of
microfabrication with the benefits of millimeter
scale components.
2. DESIGN
Vibration harvesters have been analyzed
extensively in literature [3,4,5]. Although some
discussion remains on the optimization strategy,
the following design rules are generally accepted.
2.1 Mechanical Design
The mechanical design of a harvester deals with
the coupling of the motion of the vibration to the
mechanical port of the transducer. The mechanical
port of the transducer is connected to the vibrating
package and the seismic mass. To reduce damping
the mass m is suspended in the harvester. The
suspension itself however shows a spring-like
behavior, resulting in resonance at the natural
frequency Zn.
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The maximum mechanical power that can be
extracted by the mechanical system at resonance
is given by [4,5]:
1
(1)
Pmax
mZ n ax max
2
In this formula the maximum allowed
displacement of the mass relative to the package,
xmax is taken into account, for a given vibration
with pulsation Zn and acceleration a. This power
increases linearly with the size of the seismic
mass. A seismic mass with a higher inertia will
allow the designer to extract more energy from the
vibration, while resonance can be used to match
the small amplitudes or forces of the vibration to
the needs of the transducer.
2.2 Transducer Design
The transducer is the key component of the
energy harvester. An optimal design matches the
mechanical impedance of the transducer to the
characteristics of the mass-spring system.
Likewise, its electrical impedance is matched to
the specifications of the power electronics of the
autonomous system. Although different types of
electromechanical transducers exist [6], their
working principles coincide: energy is stored in
the electric field or in the magnetic flux. A change
in geometry will then result in a change of stored
energy, at the expense of the mechanical energy
needed to alter the geometry.
The electrodynamic transducer presented in this
work uses the energy stored in the flux B of a
permanent magnet. This flux is coupled to the
electric circuit by a coil (Fig. 1), a change in
geometry will induce a change in the coupled flux
I , which in turn will generate an e.m.f. across the
coil:
dI
d
e.m. f . ³ Bds
dt
dt A
dA
dA
NB
NB z
(2)
dt
dz
In equation (2) the coupled area A changes over
time as the mechanical configuration changes.
The velocity of the mass is indicated by Ī. The
current i that is induced through the electric load
R by the e.m.f. will in turn induce a counteracting
force on the magnet. The factor * NB dA defines
dz
the ratio between the speed of the mass and the
generated voltage.
86
An optimal transducer is designed in such a way
to electromechanically damp the motion of the
mass to its maximum displacement xmax, when the
input impedance R of the power electronics is
applied. The mechanical damping factor needed to
reach the power of equation (1) is given by:
*2
a
(3)
9g
2
2 RmZ n 2Z n x max
The optimal transformation factor follows:
aRm
(4)
*
Z n x max
2.3 Design of the harvester
In order to optimize the generated power at a
frequency of 100 Hz, the seismic mass has to be
maximized within the small volume of the
generator. The NdFeB magnets have a density of
7400 kg/m3 as opposed to the density of silicon
(2300 kg/m3). They are incorporated on the
seismic mass. This is achieved by etching pockets
in the mass (Fig. 2).
i
o
e.m.f.
B
A
S
N
N turns
z(t)
Fig. 1: Electromagnetic transduction mechanism
used in the vibration harvester.
NdFeB magnets
Magnet
Pockets
Perforation
Suspension
Polymer
bonding
Meandering
Coil
Fig. 2: Exploded view of the proposed device
In this way the mass is increased from 40 mg up
to 80 mg. The suspension of the mass is shaped in
order to obtain a spring constant of 33 N/m.
The magnets are off-the-shelf components of
1 mm3, with a residual flux density of 1.2 T [7].
The pockets that hold the magnets are perforated
at the position of the poles of the magnets. The
flux lines are slightly condensed due to the
diamagnetic character of silicon.
Underneath the floating mass a coil has been
patterned on the bottom wafer. This coil has a
meandering shape: the coupled flux of the magnet
to the coil changes every time the poles of the
magnet cross the meandering metal line. The
result is an increase of the transformation factor *
by increasing the factor dA . As a consequence
dz
the frequency of the generated signal will be a
multiple of the input frequency. The same
approach has been used in literature for
electrostatic vibration harvesters [5,8] and
piezoelectric harvesters [9]. The meandering
copper coil can be wound several times to further
increase the transformation factor (factor N in
equation (2)). Based on equation (1) the maximum
achievable mechanical power is estimated up to
200PW for a 1g vibration at 100Hz.
3. PROCESS FLOW
The prototyping of the vibration harvester is
based upon the same process flow already used
for electrostatic generators [5].
The device consists of 3 wafers, of which the top
wafer only serves as a cap for the device. Pyrex
glass was selected as material for the bottom
wafer, for demonstration purposes. The thermal
match between silicon and Pyrex is a necessity to
minimize stresses after bonding. At first a 300 nm
copper layer is deposited on the wafer and
subsequently patterned in the meandering shape.
As this prototype is intended as a proof of
concept, its design and fabrication have been
simplified, at the expense of a loss in
performance. Only one metal layer was deposited,
while the copper coil was wound 3 to 6 times to
increase the transformation factor (Fig. 3). In a
next step the BCB is spun and patterned on the
wafer, which will later be used for polymer
bonding of the wafers.
After realization a series impedance of 3.3k:
was measured (6 windings), while the inductance
was limited to 200 PH. This wafer is next diced
halfway its thickness. In this way the wafer can
still be processed as a whole, while dicing can be
done manually by snapping across the pre-diced
lines. The middle wafer consists of silicon that
has been coated with a 150 nm Si3N4 layer on
both sides. This layer is patterned with the springs
and perforation holes. Next the wafer is etched in
KOH (35% at 50°C), where the Si3N4 layer was
used as a hard mask. Although this step could as
well be performed using DRIE, KOH was chosen
as a fast alternative for prototyping. The springs
are then oriented along the {100} direction (Fig.
4). The combination of a 30 Pm wide and 15 Pm
high folded beam of 2.3 mm should result in a
resonance frequency of 100 Hz, while allowing a
displacement of 800 Pm.
The two wafers are next bonded by a 3000 N
force at 250 degrees. The BCB bond is now KOHresistant, and the glass wafer protects the freshly
etched springs. After patterning the top side of the
waferstack, the masses and magnet pockets are
etched, again by 35% KOH, until a membrane of
30 Pm remains. Finally the devices are released in
a short DRIE-etch step. The magnets are manually
mounted, and glued to the top of the mass.
6 copper coils
BCB
Contact pads
Fig. 3: Top view of the bottom wafer, illustrating
the 6 meandering copper coils.
Fig. 4:The springs are etched in KOH. Due to
their {100} orientation a 90° angle was obtained
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4. DISCUSSION
The device as presented has not been
optimized, neither in reliable fabrication nor in
optimal matching towards power electronics
circuitry, until the concept has been proved to
work. As a result many improvements can be
found for optimization of the power output.
A first improvement would be to increase the
number of coil windings N in order to obtain a
better coupling, while the thickness of the copper
layer could be increased to manage the parasitic
series resistance of the coil. This measure could
be extended towards depositing multiple layers of
coils on the glass wafer, each insulated by e.g.
BCB. A second improvement consists in filling
the perforated holes with a ferromagnetic material
(e.g. Ni) for a better guiding of the magnetic flux
towards the coils. As a result the pitch of the
meandering coil can be further decreased and the
transformation factor is further increased.
5. CONCLUSIONS
A prototype of an electrodynamic vibration
harvester has been designed and fabricated.
Through the use of 1 mm3 NdFeB magnets in the
seismic mass of the generator the mechanical
capturing of energy has been improved at 100 Hz.
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